Download Nonlinear Time Series Analysis of Economic and Financial by Andrew J. Filardo, Stephen F. Gordon (auth.), Philip Rothman PDF

By Andrew J. Filardo, Stephen F. Gordon (auth.), Philip Rothman (eds.)

Nonlinear Time sequence research of financial and monetary Data presents an exam of the flourishing curiosity that has built during this sector over the last decade. The consistent topic all through this paintings is that normal linear time sequence instruments depart unexamined and unexploited economically major positive factors in often used facts units. The booklet includes unique contributions written by means of experts within the box, and provides a mixture of either utilized and methodological papers. it is going to be worthy to either professional veterans of nonlinear time sequence research and people looking for an informative panoramic examine front-line advancements within the area.

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Improved estimates of the transition probabilities are simple functions of the smoothed probabilities. The set of updated values constitutes 0[1]; we repeat the process until some convergence criterion is satisfied. lt-2) + c~2). l(1)) = 1/11 ) (Yt-1 Ci,t '" N(O, (a(i))2), i = 1,2. l(2), 1>(11), 1>(12), 1>(21), 1>(22), a(l), a(2), p(l1), p(22). A single iteration of the EM algorithm starts by executing the filter. g. s; = 1 implies St = 1, St-1 = 1, St-2 = 1. l(1»)]2/2(a(1»)2}. We next execute the smoother to find a probability series that is less volatile than 40 BRUCE MIZRACH AND JAMES WATKINS that provided by the filter (32) while integration yields (33) With smoothed inferences available, coefficients are updated numerically by minimizing the sum of weighted squared residuals [/P), p,(2), cP] = arg min {2:;=3 2:~=1 (v~k»)2 where cP = [4>(11),4>(12),4>(21), ¢P2)] .

1982). K. Inflation," Econometrica, 50,987-1007. Filardo, Andrew 1. (1994). "Business Cycle Phases and their Transitional Dynamics," Journal ofBusiness and Economic Statistics, 12,299-308. Ghysels, Eric (1994), "On the Periodic Structure of the Business Cycle," Journal of Business and Economic Statistics, 12,289-98. Goldfeld, Stephen M. and Richard E. Quandt (1973). "A Markov Model for Switching Regressions," Journal of Econometrics, 1,3-16. Goodwin, Thomas H. (1993). "Business Cycle Analysis with a Markov Switching Model," Journal ofBusiness and Economic Statistics, 11,331-39.

Estimation procedures are described in section 3, and the accompanying algorithms in sections 4 and 5. The relative merits of the two algorithms is discussed in section 6 and computational speed comparisons are presented in section 7. htrnl 2. Time Series Models of Changes in Regime A brief description of the Markov-switching (hereafter MS) framework is helpful to establish notation and vocabulary. The following description follows closely that of Hamilton (1993). Consider for simplicity a first order autoregression where the mean value around which this series clusters may take on one of two values, 1-£(1) and 1-£(2): Yt - I-£t = ¢(Yt-l - I-£t-l) + ct· (1) Suppose further that ct ~ iidN(O, (72).

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